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Description of Liquid Tank of LM-900 Lab

Introduction

This document gives a short description of the liquid tank of the LM-900 Lab. The inbuilt Fuji PYZ5 PID-controller at the right of the panel is not described.

Layout

Figure 1 shows the liquid tank.

Figure 1: LM-900 Liquid tank

Figure 2 below shows the panel of the tank.

Figure 2: The panel of the tank

Operation

Power

The tank is powered via a mains switch, see Figure 1.

Pump (inflow)

A pump fills the tank with water from the reservoir. The pump speed can be controlled by a voltage signal in the range 0 - 5V.

The pump can be controlled by an external voltage signal at the FROM PC connector, see Figure 2 above, or by the inbuilt Fuji level controller. The LOCAL/PC switch, see Figure 2, is used to select between external control or internal control.

Valve (outflow)

Water flows from the bottom of the tank to the reservoir via a pipe in which there is a manually operated valve, see Figure 1.

Level measurement

The water level is measured by a level sensor. The measurement is a voltage signal in the range 0 - 5V available at the TO PC connector, see Figure 2. This voltage range corresponds to a level range of 0 - 20 cm, approximately (unless you need a more accurate relation, you can assume this range in your applications).

The level sensor is based on measurement of the air pressure in the air pipe. The higher level - the higher hydrostatic presssure at the pipe outlet at the bottom. The pipe must always be filled by air - no water. You adjust the purge meter to ensure that the pipe is filled by air (bubbles should bee seen from the pipe).

Connectors, switches, and indicators

See Figure 2.

  • The FROM PC connectors (the upper is plus, and the lower is minus or ground): Connect here the analog output (AO) signal from the I/O equipment (e.g. DAQ card, DAQPad, FieldPoint).
  • The TO PC connector (the upper is plus, and the lower is minus or ground): Connect here the analog input (AI) signal to the I/O equipment.
  • The LOCAL/PC switch:
    • In PC position measurement and control is via I/O equipment (as PC with I/O card).
    • In LOCAL position the internal PID controller Fuji PYZ5 PID-controller is used for control.
  • Other connectors are for interlocking functions (normally not used in simple applications).
  • LED indicators (light emitting diodes) PV and OUT are for indicating level measurement (PV = process value) and control signal (OUT).

Mathematical model

Here are a couple of mathematical models of the water tank which may be appropriate, depending on the purpose of the model:

If the model is to be used for model-based controller tuning and for design of estimators (soft-sensors), as observers or Kalman-filters, the following model can be used:

A*dx/dt = K*(u - u0) - Fout      (Eq. 1)

x [cm] is the level. u [V] is the pump control signal to the pump. u0 is the bias voltage needed to get any flow (with u less than u0 there is no flow into the tank). A [cm2] is the cross-sectional area. K [(cm3/s)/V] is the pump gain. Fout [cm3/s] is the outflow through the valve.

If the model is to be used in a simulator, the following somewhat more complicated model may be used as it is more accurate than the above model:

A*dx/dt = K1*(u - u0) - K2*sqrt(rho*g*h)        (Eq. 2)

where

Fout = K2*sqrt(rho*g*h)         (Eq. 3)

is the outflow. Eq. 3 stems from the standard valve characteristic expressing the relation between pressure drop, rho*g*h, across the valve and the flow through the valve. rho is the densitity of the water, and g is the gravity constant. Valve constant K2 depends on the opening of the valve, but if the opening is constant, K2 is constant.

How can you find good values of the model parameters A, K, K1 and K2? A can be calculated from the measured dimension of the tank. One simple way to find K, K1 and K2 is by simulating the tank (you can fancy the rest of the procedure yourself :-). Alternatively, you can use the least squares method to find these parameters.

Note that you can reduce the number of parameters by dividing Eq. 1 and Eq. 2 by A, but this may not be so important since A is quite easy to find.

Updated 25. March 2010 by Finn Haugen (Finn.Haugen@hit.no).